A day in London

If I only had a day for seeing London, I would definitely take one of the double-decker bus tours. It's the best way to see all the major sights in one trip and you can jump on and off as you wish. The ticket usually includes a free river cruise and it costs about 22 pounds. Buses run every 20-30 minutes. I recommend to avoid rush hours.
I would also go shopping to Harrod's, especially if they are in the sales. I honestly think the visit is worthwhile, the store is amazing, especially the food and the toys departments.
I would finish wandering around Hyde Park, which is closed to the store.
I would have lunch in any of the pubs around the city. The menus are cheap and quite healthy compared with the typical fish & chips or mashed potatoes stuff.